Essentially all modern medical scanners export data in this format.
This fantastic site will let you view (after upload) DICOM images in a web browser:
There are a number of accessible (ie not clinical radiology priced) viewers available, the best of the lot for general use being Osirix [1] (OS X only), and ClearCanvas [2] (Windows only). Ginkgo CADx [3] and Mint viewer [4] are also good, and both cross-platform.
There are several well-regard open-source libraries for DICOM: gdcm [5] and DCMTK [6]. Widely used open-source medical image visualization SDKs with DICOM support include MITK [7] and 3D Slicer [8] (the afore-mentioned ClearCanvas is also an SDK in some sense).
[edit: formatting and add link]
1. http://en.wikipedia.org/wiki/OsiriX
2. http://www.clearcanvas.ca/dnn/
4. http://www.mint-medical.de/
5. http://en.wikipedia.org/wiki/GDCM